Question: $-8ij + 4ik + i - 9 = 7j - 4$ Solve for $i$.
Combine constant terms on the right. $-8ij + 4ik + i - {9} = 7j - {4}$ $-8ij + 4ik + i = 7j + {5}$ Notice that all the terms on the left-hand side of the equation have $i$ in them. $-8{i}j + 4{i}k + 1{i} = 7j + 5$ Factor out the $i$ ${i} \cdot \left( -8j + 4k + 1 \right) = 7j + 5$ Isolate the $i$ $i \cdot \left( -{8j + 4k + 1} \right) = 7j + 5$ $i = \dfrac{ 7j + 5 }{ -{8j + 4k + 1} }$